There are plenty of nice routes for cycling on our doorstep. We cycled from Southampton to Portsmouth along the National Cycle Network (NCN) Route 2, which runs all the way from Dover to Penzance.
We live in Totton, from where it is a short ride to West Quay in Southampton, passing the Isle of Wight Ferry terminal, just following the NCN 2 route markers.
We went over the Itchen Bridge near the football stadium, then through Woolston, along Weston Shore past Netley to Hamble Le Rice. We then took the Pink Ferry across the River, cycling through the countryside, which has plenty of nice places to stop along the way, such as Titchfield Haven.
We took our time, cycling gently and left home at 10:00hrs, eventually arriving at the Gosport Ferry terminal by 14:00hrs, which also included a 40 min coffee stop in Hamble Le Rice. Our return was a little easier, returning to Southampton Central Station by train and then the brief bike ride home.
We would advise that you check online first for details on when the Pink Ferry service is operating and for bicycle space on the trains.